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arXiv · 1112.4148

On hyperbolicity and tautness modulo an analytic subset of Hartogs domains

Do Duc Thai·Pascal J. Thomas·Nguyen Van Trao·Mai Anh Duc
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Abstract

Let $X$ be a complex space and $H$ a positive homogeneous plurisubharmonic function $H$ on $X\times\C^m$. Consider the Hartogs-type domain $\Omega_{H}(X):=\{(z,w)\in X\times \C^m:H(z,w)<1 \}$. Let $S$ be an analytic subset of $X$. We give necessary and sufficient conditions for hyperbolicity and tautness modulo $S\times \C^m$ of $\Omega_{H}(X)$, with the obvious corollaries for the special case of Hartogs domains.

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Do Duc Thai, Pascal J. Thomas, Nguyen Van Trao, Mai Anh Duc. 2011-12-18. On hyperbolicity and tautness modulo an analytic subset of Hartogs domains. https://doi.org/10.1090/s0002-9939-2013-11645-x

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